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Question

Find the acceleration of the system shown in the figure.


A
g7
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B
g3
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C
2g5
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D
2g7
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Solution

The correct option is D 2g7
Let us first draw the free body diagrams of 20 kg, 5 kg and 10 kg block.

From condition of equilibrium, we have
20 gT1=20a...............(i)
And,
T1T2=5a..................(ii)
On adding (i) & (ii), we have
20gT2=25a...........(iii)
Also, we have
T210g=10a.........(iv)
On adding (iii) & (iv) we have
20g10g=35aa=10g35=2g7

Alternate:
Let us consider all three bodies as a system.
As the force on the left side is more (i.e. 20g>10g) so, the system will move in the left direction.




From the figure, acceleration of the system will be
a=Effective forceTotal mass
a=(20g10g)35=10g35=2g7

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